Apply subsurf modifier to only part of an object
This is possible on some modifiers via vertex groups, however this is not possible with subsurf modifier.
You could instead try some of these:
For reference, here is the original subsurfed mesh:


Separate the pedestal and goblet into different objects (P &gt; By Selection). E.g. by separating the face of the cube on the +X axis:


You can Split off geometry in Edit Mode with Y. This will give basically the same result as Separate, but within a single object:


You could also use the Edge Split modifier the same way, by either using Ctrl + E &gt; Mark Sharp, or with the Edge Angle property.

Use supporting geometry (i.e. edgeloops) to make edges less round. You could use Ctrl + R to add loopcuts, or use Ctrl + B to bevel edges (using the mousewheel to adjust the number of segments). E.g. bevel with 2 segments:


Use Mean crease to make edges less round (Shift + E). E.g. with a Crease weight of 1: